Is the role of the boxed condition $z'(t)neq 0$ to avoid going back?











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The role of the boxed condition $z'(t)neq 0$ is to avoid going back, isn't it?






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    The role of the boxed condition $z'(t)neq 0$ is to avoid going back, isn't it?






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      enter image description here



      The role of the boxed condition $z'(t)neq 0$ is to avoid going back, isn't it?






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      The role of the boxed condition $z'(t)neq 0$ is to avoid going back, isn't it?






      complex-analysis curves complex-integration plane-curves




      complex-analysis curves complex-integration plane-curves






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          No. It is so that the velocity is never $0$, which implies that we can parametrize the curve by the arc length. It also implies that $zbigl([a,b]bigr)$ has no “corners”, which corresponds to the idea of a smooth curve.






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            No. It is so that the velocity is never $0$, which implies that we can parametrize the curve by the arc length. It also implies that $zbigl([a,b]bigr)$ has no “corners”, which corresponds to the idea of a smooth curve.






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              No. It is so that the velocity is never $0$, which implies that we can parametrize the curve by the arc length. It also implies that $zbigl([a,b]bigr)$ has no “corners”, which corresponds to the idea of a smooth curve.






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                up vote
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                No. It is so that the velocity is never $0$, which implies that we can parametrize the curve by the arc length. It also implies that $zbigl([a,b]bigr)$ has no “corners”, which corresponds to the idea of a smooth curve.






                share|cite|improve this answer












                No. It is so that the velocity is never $0$, which implies that we can parametrize the curve by the arc length. It also implies that $zbigl([a,b]bigr)$ has no “corners”, which corresponds to the idea of a smooth curve.







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